Basic properties
| Modulus: | \(4719\) | |
| Conductor: | \(4719\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4719.cu
\(\chi_{4719}(116,\cdot)\) \(\chi_{4719}(194,\cdot)\) \(\chi_{4719}(272,\cdot)\) \(\chi_{4719}(545,\cdot)\) \(\chi_{4719}(623,\cdot)\) \(\chi_{4719}(662,\cdot)\) \(\chi_{4719}(701,\cdot)\) \(\chi_{4719}(974,\cdot)\) \(\chi_{4719}(1052,\cdot)\) \(\chi_{4719}(1091,\cdot)\) \(\chi_{4719}(1130,\cdot)\) \(\chi_{4719}(1403,\cdot)\) \(\chi_{4719}(1481,\cdot)\) \(\chi_{4719}(1520,\cdot)\) \(\chi_{4719}(1559,\cdot)\) \(\chi_{4719}(1832,\cdot)\) \(\chi_{4719}(1910,\cdot)\) \(\chi_{4719}(1949,\cdot)\) \(\chi_{4719}(1988,\cdot)\) \(\chi_{4719}(2261,\cdot)\) \(\chi_{4719}(2378,\cdot)\) \(\chi_{4719}(2690,\cdot)\) \(\chi_{4719}(2768,\cdot)\) \(\chi_{4719}(2807,\cdot)\) \(\chi_{4719}(2846,\cdot)\) \(\chi_{4719}(3197,\cdot)\) \(\chi_{4719}(3236,\cdot)\) \(\chi_{4719}(3275,\cdot)\) \(\chi_{4719}(3548,\cdot)\) \(\chi_{4719}(3626,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1574,3511,4357)\) → \((-1,e\left(\frac{19}{110}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4719 }(116, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{46}{55}\right)\) |